{"title":"Numerosity depends on normalized contrast energy: Review and square-root law model","authors":"Quan Lei , Adam Reeves","doi":"10.1016/j.visres.2023.108280","DOIUrl":null,"url":null,"abstract":"<div><p>The perceived numerosity of many randomly-located items of fixed contrast depends on the integrated contrast energy (CE) of the display. We show here that a model based on √(CE), normalized by contrast amplitude, can fit numerosity judgment data in various tasks and over a wide range of numerosities. The model shows that judged numerosity increases linearly with √(N), where N is the number of displayed items above the subitization range, and can explain: 1) the general underestimation in absolute judgement of numerosity; 2) the contrast independence (constancy) of numerosity judgment in segregated displays, i.e., judged numerosities are not affected by item contrast; 2) a contrast-dependent illusion where the numerosity of higher-contrast items is further underestimated when intermingled with lower-contrast items; and 3) both the threshold and sensitivity of numerosity discrimination between displays of N and M items. The nearly perfect fit of numerosity judgment data by a square-root law over a wide range of numerosities, including the range typically described by Weber’s law, but excluding subitization, suggests that normalized contrast energy might be the prevailing sensory code underlying numerosity perception.</p></div>","PeriodicalId":23670,"journal":{"name":"Vision Research","volume":null,"pages":null},"PeriodicalIF":1.5000,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Vision Research","FirstCategoryId":"102","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0042698923001049","RegionNum":4,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"NEUROSCIENCES","Score":null,"Total":0}
引用次数: 0
Abstract
The perceived numerosity of many randomly-located items of fixed contrast depends on the integrated contrast energy (CE) of the display. We show here that a model based on √(CE), normalized by contrast amplitude, can fit numerosity judgment data in various tasks and over a wide range of numerosities. The model shows that judged numerosity increases linearly with √(N), where N is the number of displayed items above the subitization range, and can explain: 1) the general underestimation in absolute judgement of numerosity; 2) the contrast independence (constancy) of numerosity judgment in segregated displays, i.e., judged numerosities are not affected by item contrast; 2) a contrast-dependent illusion where the numerosity of higher-contrast items is further underestimated when intermingled with lower-contrast items; and 3) both the threshold and sensitivity of numerosity discrimination between displays of N and M items. The nearly perfect fit of numerosity judgment data by a square-root law over a wide range of numerosities, including the range typically described by Weber’s law, but excluding subitization, suggests that normalized contrast energy might be the prevailing sensory code underlying numerosity perception.
期刊介绍:
Vision Research is a journal devoted to the functional aspects of human, vertebrate and invertebrate vision and publishes experimental and observational studies, reviews, and theoretical and computational analyses. Vision Research also publishes clinical studies relevant to normal visual function and basic research relevant to visual dysfunction or its clinical investigation. Functional aspects of vision is interpreted broadly, ranging from molecular and cellular function to perception and behavior. Detailed descriptions are encouraged but enough introductory background should be included for non-specialists. Theoretical and computational papers should give a sense of order to the facts or point to new verifiable observations. Papers dealing with questions in the history of vision science should stress the development of ideas in the field.